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Solve the equation 2x^{2} - x - 6 = 0

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2x^{2} - x - 6 = 0

2x^{2} - x - 6 = 0

2x^{2} - 4x + 3x - 6 = 0

(2x^{2} - 4x) + (3x - 6) = 0

2x(x - 2) + 3(x - 2) = 0

(2x + 3) (x - 2) = 0

2x + 3 = 0 and x - 2 = 0

2x = -3 and x = 2

x = -3/2 and x = 2

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2x^{2} - x - 6 = 0

Divide through by 2

x^{2} - x/2 - 3 = 0

sum of root = -1/2

product of root = -3.

Hence, we look for two numbers when added gives us -1/2 and when multiplied gives us -3

Let the two numbers be: 3/2 and -2.

The equation becomes:

x^{2} + 3x/2 - 2x - 3 = 0

(x^{2} + 3x/2) - (2x + 3) = 0

x(x + 3/2) - 2(x + 3/2) = 0

(x - 2) (x + 3/2) = 0

x - 2 = 0 and x + 3/2 = 0

x = 2 and x = -3/2

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